Spin-wave interactions in quantum antiferromagnets

TL;DR

This paper investigates spin-wave interactions in quantum antiferromagnets by reformulating magnon operators into Hermitian fields, deriving an effective action, and comparing renormalization group results with the nonlinear sigma model.

Contribution

It introduces a new parameterization of magnon operators into Hermitian fields and derives an effective action, providing insights into spin-wave interactions and their long-wavelength behavior.

Findings

Two-body interaction vertex vanishes at long wavelengths

Renormalization group flow matches nonlinear sigma model results

Effective action for staggered fluctuations derived

Abstract

We study spin-wave interactions in quantum antiferromagnets by expressing the usual magnon annihilation and creation operators in terms of Hermitian field operators representing transverse staggered and ferromagnetic spin fluctuations. In this parameterization, which was anticipated by Anderson in 1952, the two-body interaction vertex between staggered spin fluctuations vanishes at long wavelengths. We derive a new effective action for the staggered fluctuations only by tracing out the ferromagnetic fluctuations. To one loop order, the renormalization group flow agrees with the nonlinear-$\sigma$-model approach.